= Student t random-effect model
{c}
{title2=$\beta_j\mid\mu,\psi\sim\mu+\psi t_\nu$}
A <Student t random-effect model> assigns <Student's t-distributions> to exchangeable study effects, allowing heavier tails than a <normal distribution> hierarchy. An equivalent <Gaussian scale mixture> is $\lambda_j\sim\chi^2_\nu$, $\beta_j\mid\lambda_j,\mu,\psi\sim N(\mu,\nu\psi^2/\lambda_j)$, with independent latent draws. For $\nu>2$ the <variance> is $\nu\psi^2/(\nu-2)$, so $\psi$ is a scale rather than a <standard deviation>. Small latent precisions weaken shrinkage for atypical studies while retaining <partial pooling> for the rest.
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